The mean forces exerted by waves on floating or submerged bodies with applications to sand bars and wave power machines

Water waves transport both energy and momentum, and any solid body which absorbs or reflects wave energy must absorb or reflect horizontal momentum also. Hence the body is subject to a mean horizontal force. In low waves, the force may be calculated immediately when the incident, reflected and transmitted wave amplitudes are known. For wave power devices the mean force can be large, so that anchoring presents practical problems. Experiments with models of the Cockerell wave-raft and the Salter ‘duck’ accurately confirm the predicted magnitude of the force at low wave amplitudes. For steeper waves, however, the magnitude of the force can be less than that given by linear theory. By experiments with submerged cylinders, it is shown that this is due partly to the presence of a free second harmonic on the down-wave side. In breaking waves, it is confirmed that the mean force on submerged bodies is sometimes reduced, and even reversed. An explanation is suggested in terms of the ‘wave set-up’ produced by breaking waves. Submerged cylinders act as a kind of double beach. A negative mean force arises from an asymmetry in the breaking waves, associated with a time-delay in the response to the change in depth. Similar arguments apply to submerged reefs and sand bars. Experiments with a model bar show that long low waves propel the bar towards the shore, whereas steep, breaking waves propel it seawards. This is similar to the observed behaviour of off-shore sand bars. The existence of a horizontal momentum flux (or radiation stress) in water waves is demonstrated by using it to propel a small craft.